Methods of Preserving Symmetry in Model Updating

1995 ◽  
Vol 117 (3A) ◽  
pp. 349-354
Author(s):  
M. J. Lam ◽  
D. J. Inman
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Natural Frequencies ◽  
Model Updating ◽  
Mode Shapes ◽  
Modal Parameter ◽  
Modal Data ◽  
Model Correction ◽  
Damped Systems ◽  
Stiffness And Damping

This work examines the model updating technique for both conservative and nonproportionally damped systems. In model updating, also referred to as model correction, the analytical model is updated until it agrees with the experimental data available. In this paper it is assumed that the measured modal data, i.e., natural frequencies and in some instances mode shapes, disagrees in part with the modal parameter predicted by the analytical model. Many model updating schemes tend to produce nonsymmetric updated stiffness (and damping) matrices. The methods presented here focus on retaining the desired symmetry in the updated model

Symmetric Model Correction of Mechanical Systems

1993 ◽  
Author(s):  
Marca Lam ◽  
Daniel J. Inman ◽  
Andreas Kress
Keyword(s):  
Analytical Model ◽  
Model Updating ◽  
Symmetric Model ◽  
Simple Method ◽  
Modal Data ◽  
Model Correction ◽  
Systems Model ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Damped Systems

Abstract This work examines the model updating problem for simple nonconservative proportionally damped systems. Model correction, also called model updating, refers to the practice of adjusting an analytical model until the model agrees with measured modal data. The specific case examined here assumes that natural frequencies and modal damping ratios are available from vibration tests and that the measured data disagrees in part with the modal data predicted by an analytical model. Most model correction schemes tend to produce updated damping and stiffness matrices which are asymmetric. The simple method presented here focuses on retaining the desired symmetry in the updated model.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

L1 Regularized Model Updating for Structural Damage Detection

2018 ◽  
Vol 18 (12) ◽  
pp. 1850157 ◽  
Author(s):  
Yu-Han Wu ◽  
Xiao-Qing Zhou
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Model Updating ◽  
Regularization Parameter ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Modal Data ◽  
Vibration Data ◽  
Stiffness Reduction ◽  
Regularized Model

Model updating methods based on structural vibration data have been developed and applied to detecting structural damages in civil engineering. Compared with the large number of elements in the entire structure of interest, the number of damaged elements which are represented by the stiffness reduction is usually small. However, the widely used [Formula: see text] regularized model updating is unable to detect the sparse feature of the damage in a structure. In this paper, the [Formula: see text] regularized model updating based on the sparse recovery theory is developed to detect structural damage. Two different criteria are considered, namely, the frequencies and the combination of frequencies and mode shapes. In addition, a one-step model updating approach is used in which the measured modal data before and after the occurrence of damage will be compared directly and an accurate analytical model is not needed. A selection method for the [Formula: see text] regularization parameter is also developed. An experimental cantilever beam is used to demonstrate the effectiveness of the proposed method. The results show that the [Formula: see text] regularization approach can be successfully used to detect the sparse damaged elements using the first six modal data, whereas the [Formula: see text] counterpart cannot. The influence of the measurement quantity on the damage detection results is also studied.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Xiaolei Song ◽  
Haijun Liu
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Classical Problem ◽  
Mode Shapes ◽  
Wide Range ◽  
Fundamental Understanding ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Symmetric And Antisymmetric Modes ◽  
Good Agreement

Abstract Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

Identification of Structural Property Degradations by Computational Model Updating

2007 ◽  
Vol 347 ◽  
pp. 19-34 ◽  
Author(s):  
Michael Link ◽  
Stefan Stöhr ◽  
Matthias Weiland
Keyword(s):  
Experimental Data ◽  
Computational Model ◽  
Structural Property ◽  
Test Data ◽  
Measurement Errors ◽  
Structural Damage ◽  
Model Updating ◽  
Moving Load ◽  
Mode Shapes ◽  
Damage Scenarios

Computational model updating techniques are used to adjust selected parameters of finite element models in order to make the models compatible with experimental data. This is done by minimizing the differences of analytical and experimental data, for example, natural frequencies and mode shapes by numerical optimization procedures. For a long time updating techniques have also been investigated with regard to their ability to localize and quantify structural damage. The success of such an approach is mainly governed by the quality of the damage model and its ability to describe the structural property changes due to damage in a physical meaningful way. Our experience has shown that due to unavoidable modelling simplifications and measurement errors the changes of the corresponding damage parameters do not always indicate structural modifications introduced by damage alone but indicate also the existence of other modelling uncertainties which may be distributed all over the structure. This means that there are two types of parameters which have to be distinguished: the damage parameters and the other parameters accounting for general modelling and test data uncertainties. Although these general parameters may be physically meaningless they are necessary to achieve a good fit of the test data and it might happen that they cannot be distinguished from the damage parameters. For complex industrial structures it is seldom possible to generate unique structural models covering all possible damage scenarios so that one has to expect, that the parameters introduced for describing the damage will not be fully consistent with the physical reality. This is the reason why in the scientific community there is still some doubt if model based techniques can be used at all for practical purposes of damage detection and quantification under in-situ environment conditions. In the present paper we summarize the methodology of computational model updating and report about our experience with damage identification exemplified by practical examples. A new technique and an application of localising and quantifying the damage from updating the parameters of the damaged and the undamaged models simultaneously using the differences of the test data from the damaged and the undamaged structure is also presented. In this application we used the deflections (influence lines) of a beam structure measured under a slowly moving load.

scholarly journals Model Updating of Friction Stir Welding for Aluminium and Magnesium Plate Structure

2018 ◽  
Vol 150 ◽  
pp. 04004 ◽  
Author(s):  
Nazrotul Afina Nazri ◽  
Mohd Shahrir Mohd Sani ◽  
Muhammad Nasiruddin Mansor ◽  
Siti Norazila Zahari
Keyword(s):  
Friction Stir Welding ◽  
Natural Frequencies ◽  
Model Updating ◽  
Mode Shapes ◽  
Average Error ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Friction Stir ◽  
Dissimilar Friction Stir Welding ◽  
Al 7075

Friction stir welding (FSW) of aluminium and magnesium alloys face high demands in automotive and aerospace application due to its advanced and lightweight properties. FSW is an emerging solid state joining process in which the material that is being welded does not melt and recast. The main objectives of this project are to perform model updating based on finite element analysis (FEA) and experimental modal analysis (EMA) of dissimilar material of aluminium alloy AL 7075 and magnesium alloy AZ 31B. Modal properties such as natural frequencies, mode shapes are obtained and compared between FEA and EMA. The discrepancies of first five modes natural frequencies are below than 10% and the model updating have been conducted to minimize the error between two methods. This model updating are based on sensitivity analysis in order to make sure which parameters are given more influence in this structural dynamic analysis. Young’s modulus and Poisson’s ratio both materials are selected in the model updating process. After perform model updating, total average error of the natural frequencies of dissimilar friction stir welding plate is improved significantly.

Improved Inverse Eigensensitivity Method for Structural Analytical Model Updating

1995 ◽  
Vol 117 (2) ◽  
pp. 192-198 ◽  
Author(s):  
R. M. Lin ◽  
M. K. Lim ◽  
H. Du
Keyword(s):  
Analytical Model ◽  
Model Updating ◽  
Element Model ◽  
Small Error ◽  
Analytical Models ◽  
Engineering Structures ◽  
Modal Data ◽  
Existing Problems ◽  
Practical Engineering ◽  
True Values

In order to update analytical models of practical engineering structures, inverse eigensensitivity method (IEM) has been developed. Though it has nowadays been widely accepted, the classical inverse eigensensitivity method does have some drawbacks such as the assumption of small error magnitudes and slow speed of convergence due to the fact that the sensitivity coefficients are calculated purely based on modal data of analytical model. In the present paper, an improved inverse eigensensitivity method, which avoids the existing problems of classical inverse eigensensitivity method, has been developed. The improved method employs both analytical and experimental modal data to calculate the required eigensensitivity coefficients which are very close to their true values. The method has been further extended to the case where measured coordinates are incomplete. Practical applicability of the method has been assessed by its application to the updating of the finite element model of a plane truss structure.

scholarly journals An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
R. Belotti ◽  
R. Caracciolo ◽  
I. Palomba ◽  
D. Richiedei ◽  
A. Trevisani
Keyword(s):  
Dynamic Models ◽  
Model Updating ◽  
Body Motion ◽  
Transformation Model ◽  
Mode Shapes ◽  
Deformation Model ◽  
Flexible Link ◽  
Static Tests ◽  
State Observers ◽  
Stiffness And Damping

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes.

scholarly journals Identification of Historical Veziragasi Aqueduct Using the Operational Modal Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
E. Ercan ◽  
A. Nuhoglu
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Model Updating ◽  
Dynamic Properties ◽  
Dynamic Test ◽  
Element Model ◽  
Operational Modal Analysis ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Mode Shapes

This paper describes the results of a model updating study conducted on a historical aqueduct, called Veziragasi, in Turkey. The output-only modal identification results obtained from ambient vibration measurements of the structure were used to update a finite element model of the structure. For the purposes of developing a solid model of the structure, the dimensions of the structure, defects, and material degradations in the structure were determined in detail by making a measurement survey. For evaluation of the material properties of the structure, nondestructive and destructive testing methods were applied. The modal analysis of the structure was calculated by FEM. Then, a nondestructive dynamic test as well as operational modal analysis was carried out and dynamic properties were extracted. The natural frequencies and corresponding mode shapes were determined from both theoretical and experimental modal analyses and compared with each other. A good harmony was attained between mode shapes, but there were some differences between natural frequencies. The sources of the differences were introduced and the FEM model was updated by changing material parameters and boundary conditions. Finally, the real analytical model of the aqueduct was put forward and the results were discussed.

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